How to go from the airport to the most famous places of Beijing?

When are you going to have this trip? Simatai has not reopened yet and there is still no official informatoon about the reopening date.

Here is the way to ur destination from the airport as I know:
To Badaling, it is suggested to take shuttle bus line 2 to Yonghegong Lama Temple. At this subway station, take line 2 to Jishuitan and walk to Deshengmen to take bus no. 919 or 880 to reach directly;

To Mutianyu, you can take shuttle bus line 3 to Dongzhimen, near which you can find bus no. 867. It can diretly take you to the wall section.

To Forbidden City, shuttle bus line 1 helps. By that, get off at Dabeiyao(Guomao Bridge) and walk to Guomao Metro Station to take subway line 1 to Tiananmen East or West to walk to Forbidden City then.

To Summer Palace, it is suggested to take shuttle bus line 5 to its terminus - Zhongguancun. Then walk to Zhongguancun Subway Station to take metro line 4 to get off at Beigongmen, which is within walking distance from your destination.

Hope help!